Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ASYMPTOTIC BEHAVIOR FOR STRONGLY DAMPED WAVE EQUATIONS ON ℝ3 WITH MEMORY

  • Xuan-Quang Bui (Faculty of Fundamental Sciences Phenikaa University) ;
  • Duong Toan Nguyen (Faculty of Mathematics and Natural Sciences Haiphong University) ;
  • Trong Luong Vu (VNU-University of Education Vietnam National University, Department of Mathematics FPT University)
  • Received : 2023.10.09
  • Accepted : 2024.02.05
  • Published : 2024.07.01
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Abstract

We consider the following strongly damped wave equation on ℝ3 with memory utt - αΔut - βΔu + λu - ∫0∞ κ'(s)∆u(t - s)ds + f(x, u) + g(x, ut) = h, where a quite general memory kernel and the nonlinearity f exhibit a critical growth. Existence, uniqueness and continuous dependence results are provided as well as the existence of regular global and exponential attractors of finite fractal dimension.

Keywords

Acknowledgement

This work was completed while the authors were visiting the Vietnam Institute of Advanced Study in Mathematics (VIASM). The authors would like to thank the Institute for its hospitality.

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